Optimal. Leaf size=39 \[ a^3 \log (x)+\frac {3}{2} a^2 b x^2+\frac {3}{4} a b^2 x^4+\frac {b^3 x^6}{6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {3}{2} a^2 b x^2+a^3 \log (x)+\frac {3}{4} a b^2 x^4+\frac {b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^3}{x} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (3 a^2 b+\frac {a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx,x,x^2\right )\\ &=\frac {3}{2} a^2 b x^2+\frac {3}{4} a b^2 x^4+\frac {b^3 x^6}{6}+a^3 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \[ a^3 \log (x)+\frac {3}{2} a^2 b x^2+\frac {3}{4} a b^2 x^4+\frac {b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 33, normalized size = 0.85 \[ \frac {1}{6} \, b^{3} x^{6} + \frac {3}{4} \, a b^{2} x^{4} + \frac {3}{2} \, a^{2} b x^{2} + a^{3} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.96, size = 36, normalized size = 0.92 \[ \frac {1}{6} \, b^{3} x^{6} + \frac {3}{4} \, a b^{2} x^{4} + \frac {3}{2} \, a^{2} b x^{2} + \frac {1}{2} \, a^{3} \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 34, normalized size = 0.87 \[ \frac {b^{3} x^{6}}{6}+\frac {3 a \,b^{2} x^{4}}{4}+\frac {3 a^{2} b \,x^{2}}{2}+a^{3} \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.31, size = 36, normalized size = 0.92 \[ \frac {1}{6} \, b^{3} x^{6} + \frac {3}{4} \, a b^{2} x^{4} + \frac {3}{2} \, a^{2} b x^{2} + \frac {1}{2} \, a^{3} \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 33, normalized size = 0.85 \[ a^3\,\ln \relax (x)+\frac {b^3\,x^6}{6}+\frac {3\,a^2\,b\,x^2}{2}+\frac {3\,a\,b^2\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 37, normalized size = 0.95 \[ a^{3} \log {\relax (x )} + \frac {3 a^{2} b x^{2}}{2} + \frac {3 a b^{2} x^{4}}{4} + \frac {b^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________